Transcript Rotation & Torque (97-03)

AP Physics
The angle “θ” used to represent rotational position
 Units: radians or degrees
(remember 2π rad = 360o)
θ2
Change in rotational position during
some time interval is
average angular velocity, ω.
ω
Δθ
ω
θ1
Change in angular velocity during some time interval is
average angular acceleration, α.
A compact disc (CD) rotates at high speed while a laser reads data
encoded in a spiral pattern. The disc has a radius r = 6 cm. At
some point while the data is being “read” from the disc, it spins at
7200 rpm.
1.
What is the CD’s angular velocity in radians per second?
2.
How much time is required for it to rotate through 90o?
3.
If it starts from rest and reaches full speed in 4.0 s, what is its
average angular acceleration?
If the angular acceleration is constant the same constant acceleration
equations learned previously apply to a rotating body.
Quantity
Linear
Angular
Relation
Position
Velocity
Acceleration
Constant
Acceleration
Equations
s
θ2
Δθ
*s is the arc length of a circle
*r is the radius of the circle
r
ω
θ1
The quantitative measure of the tendency of a force to cause or change
rotational motion around an axis. Torque is the product of the
magnitude of the force and the moment arm (the perpendicular
distance between the axis and the force).
Door (top view)
r
Axis of rotation
θ
F
Luigi, the amateur plumber, is unable to loosen a pipe fitting. He
decides to slip a piece of scrap pipe (a “cheater”) over the handle
of his wrench. He then applies his full weight of 900 N to the end
of the cheater by standing on it. The distance from the center of
the fitting to the point where the weight acts is 0.80 m, and the
wrench handle and cheater make an angle of 19o with the
horizontal. Find the magnitude and direction of the torque of his
weight about the center of the pipe fitting.
Translational Equilibrium
The net forces acting on an object are equal to zero.
∑F=0
Object is in translational equilibrium when it’s not accelerating.
Rotational Equilibrium
The net torques acting on an object are equal to zero.
∑
τ=0
Object is in rotational equilibrium when the angular acceleration is
zero.
Static Equilibrium
There must be both Translational Equilibrium and Rotational
Equilibrium. The sum of the torques and the sum of the forces must
both add to zero.
A uniform 40 N board supports two children weighing 500 N and 350
N. The support (often called the fulcrum) is under the center of
the board, and the 500 N child is 1.5 m from the center. How far
from the center of the board will the 350 N child be for the seesaw
to be at rotational equilibrium?
1.5 m
F = 500 N
x=?
Fulcrum
F = 350 N